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arXiv · 1511.01299

On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 Surfaces

Florian Bouyer
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Abstract

In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant quartic K3 surface contains at least $320$ conics. In this paper we analyse the field of definition of those conics as well as their Monodromy group. As a result, we prove that the moduli space $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant quartic K3 surface with a marked conic has $10$ irreducible components.

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Florian Bouyer. 2015-11-04. On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 Surfaces. https://arxiv.org/abs/1511.01299

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